FUZZY CONTROLLER AND NEURAL ESTIMATOR APPLIED TO CONTROL A SYSTEM POWERED BY THREE-PHASE INDUCTION MOTOR

8/20/2019 FUZZY CONTROLLER AND NEURAL ESTIMATOR APPLIED TO CONTROL A SYSTEM POWERED BY THREE-PHASE INDU…

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International Journal of Artificial Intelligence & Applications (IJAIA) Vol. 6, No. 4, July 2015

DOI : 10.5121/ijaia.2015.6402 17

FUZZY CONTROLLER AND NEURAL ESTIMATOR

A PPLIED TO CONTROL A S YSTEM POWERED BY

THREE-PHASE INDUCTION MOTOR

Élida Fernanda Xavier Júlio1, Simplício Arnaud da Silva2, Cícero da Rocha Souto3 and Isaac Soares de Freitas4

1Postgraduate Program in Mechanical Engineering, Federal University of Paraíba, JoãoPessoa, PB, Brazil

2Department of Electrical Engineering, Federal University of Paraíba, João Pessoa, PB,Brazil

3Department of Electrical Engineering, Federal University of Paraíba, João Pessoa, PB,

Brazil4Department of Electrical Engineering, Federal University of Paraíba, João Pessoa, PB,Brazil

A BSTRACT

In this study, a control strategy is presented to control the position and the feed rate of a table of a milling

machine powered by three-phase induction motor, when machining pieces constituted by different types of

materials: steel, brass and nylon. For development of the control strategy, the vector control technique was

applied to drive the three-phase induction machines. The estimation of the electromagnetic torque of the

motor was used to determine the machining feed rate for each type of material. The speed control was

developed using fuzzy logic Takagi-Sugeno (TS) model and the estimation of the electromagnetic torque

using the artificial neural network (ANN) of the least mean square (LMS) algorithm type. The induction

motor was fed by a three-phase voltage inverter hardware driven by a digital signal processor (DSP). Experimental results are presented.

K EYWORDS

Position Control, Feed Rate Control, Estimated Electromagnetic Torque, Fuzzy Logic, Artificial Neural

Networks

1. INTRODUCTION

Milling is a machining process which consists of removing material from a piece, in order toconstruct flat surfaces or with a certain form. The removal of material is performed intermittentlyby the combination of two movements performed simultaneously: the rotation of the cutteraround its axis and the linear movement of the milling machine table where the piece to bemachined is fixed [1].

In many of machining systems, constant values of feed rate and cutting speed are establishedthroughout the tool path in the machining of surfaces, which can be very expensive formanufacturers [2].


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Cutting parameters for machining should be monitored and adjusted automatically by selectingthem appropriately to the machining process, especially the parameters of feed rate and cuttingspeed [3, 4]. In the work [5], an algorithm to adjust the feed rate automatically was developedwith the goal of achieving maximum productivity in machining of a manufacturing line.

Difficulties as the geometric complexity of pieces, high hardness and roughness of materials areidentified in the machining of free and complex formats of surfaces. In these cases, the bestmethod to control the occurrence of impacts is to regulate and control the cutting parametersaccording to the shape and the surface structure.

One of the effective ways to improve CNC machining efficiency is to use optimal cuttingparameters. An optimization method of cutting parameters for machining free formats of surfaceswas developed by applying the adaptive control of the feed rate in [6].

Due to the need of machining systems that would provide drives with variable speed, millingmachines have increasingly been driven by three-phase induction motors. Such motors are widelyused due to their low cost, ability to operate with a variety of loads in adverse conditions,simplicity of construction and maintenance.

In three-phase induction motor, the implementation of vector control for direct field orientationallows that the position of the flux is determined by measuring the magnitudes of stator terminals:voltage and current [7].

Control strategies for milling can be developed through programming algorithms with applicationof intelligent controllers and estimators, using fuzzy logic and artificial neural network. The fuzzyand ANN techniques deal with nonlinearities easily, enable the control of complex multivariablesystems and dispense mathematical modeling of the processes.

A methodology using ANN associated to fuzzy logic was presented in thesis [8] for constructionof a machining process controller, because of analytical complexity and non-linear responses ofthis machining system.

Fuzzy logic enables the implementation of human experience in systems. The Takagi-Sugenofuzzy model is able to represent, approximate or exact shape, any nonlinear dynamics as acombination of locally valid linear models, by interpolating smoothly [9]. The TS fuzzy techniquecombines a fuzzy rule-based method and a mathematical method, using conditional propositions,whose antecedents and consequents are linguistic variables and linear equations, respectively[10].

A fuzzy control strategy for end milling process was presented in [11]. In this work, the fuzzycontroller was implemented adaptively aiming to maximize the feed rate for a slow machining ofcomplex shapes surfaces.

In the research [12], a fuzzy approach was developed to determining the optimum feed rate for

the geometric features of a piece to be milled.

The artificial neural network is a technique organized according to human neural structure, whichacquires knowledge through a learning process, with parallel and adaptive processing [13].

The LMS learning algorithm is an ANN of error minimizing, based on instant estimations of errorin the output [14]. In the first work of great relevance applying LMS algorithm [15], theinterference cancellation using adaptive filters was an important reference in the field of signaldigital processing.


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The LMS algorithm technique was used to develop an adaptive filter for reducing and eliminatingnoise of interference signals in frequency radio at work [16], due to the simplicity ofimplementation and low computational complexity of this algorithm.

In reference [17], estimation of the electromagnetic torque of a three-phase induction motor wasobtained by applying the LMS algorithm. For this, neural adaptive filters were developed toeliminate offsets in the estimation of the stator flux.

The machining system developed for the realization of this work has a vertical milling machine.The table of the milling machine is composed of two bases, one called X base and the other Ybase, powered by three-phase induction motors. In this work, the drive and control of the X basewas performed in the machining process of materials: steel, brass and nylon.

The objectives of this work are: trigger the system with specific feed rates for cutting eachmaterial; control the position and the feed rate of the X base of the milling machine table, in themachining process of pieces constituted by different types of materials, called specimens. Therotation of the cutting tool is constant in this process.

A speed controller using the TS fuzzy model is developed to control the feed rate of the X base.The estimation of the electromagnetic torque of the motor of this base is performed using ANN ofthe LMS algorithm type. A DSP is programmed to implement the control strategy of themachining system.

2. DEVELOPMENT OF THE SYSTEM

The vertical milling machine of machining system is shown in Figure 1 whose cutting tool is anend mill. The X base (upper base) of the milling machine table has a course of 200 mm. On thisbase, the specimens that were submitted to the frontal machining processes were fixed.

Figure 1. Vertical milling machine


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Two types of specimens were prepared, i.e., a specimen constituted of steel and brass, and theother constituted of steel and nylon.

The machining of a specimen generates the imposition of load to the induction motor of the Xbase. Therefore, the electromagnetic torque of this motor is estimated, in order that through thisestimation be verified the type of material machined. Thus, the specific feed rates are applied tomachining each type of material of a specimen from the signal of the estimated electromagnetictorque.

As the pitch of the X base trapezoidal spindle is 4 mm and a complete revolution of the motorshaft corresponds to 2π rad, a numerical factor of 0.032 mm/rad was obtained. The position of Xbase is determined from multiplying the angular position of rotor of the motor by 0.032 mm/rad;as well as, the feed rate of this base is obtained by multiplying the rotational speed of the rotor bythis numerical factor.

In Figure 2, the system configuration for the drive and control of the X base of the millingmachine table is schematized. In this diagram, are presented: the digital signal processor, used inthe processing, transmission and data acquisition; the hardware constituted by three-phase voltage

inverter, which feeds the three-phase induction motor of the X base; the encoder for measuringthe angular position and rotational speed of rotor of the motor, thereby obtaining the position andfeed rate of the X base; and Hall effect sensors, used to obtain the currents and voltages of themotor stator.

Besides the electrical and electronic components, in Figure 2, are represented: the control system,developed for drive and control the X base of the milling machine, and the estimation system ofthe electromagnetic torque of the motor of this base.

Figure 2. Schematic diagram for control the X base of the milling machine

2.1. Control System

The control system of the milling machine was developed in closed loop, controlling the three-phase induction motor of the X base. For this, a current controller using a proportional-integral(PI) controller, and a speed controller using a TS fuzzy model were developed.


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Figure 3. Speed fuzzy controller

The input variables Error and Derror are defined in the fuzzification step. Error is the differencebetween the reference value and the value of the rotational speed of rotor ωr , and Derror is thederivative of this error. The universes of discourse of Error and Derror comprise a normalizedrange of -1 to 1.

Each variable, Error and Derror, consists of seven pertinence functions with triangular andtrapezoidal shapes, called: negative big (NB), negative medium (NM), negative small (NS),

almost zero (AZ), positive small (PS), positive medium (PM) and positive big (PB). Thearrangements of linguistic terms of the Error and Derror are presented in Figure 4 and Figure 5,respectively, in their universes of discourse.

Figure 4. Pertinence functions of the input variable Error

Figure 5. Pertinence functions of the input variable Derror

In fuzzy inference step, the forty-nine control rules developed are inserted in Table 1. For thecomposition of each rule and the relationship between them, it was applied the max-min inferencetechnique. So, to model each sentence was used min and the relationships between rules weremodeled by applying max.


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Table 1. Table of fuzzy rules.

Derror

Error

NB NM NS AZ PS PM PB

NB iNB iNB iNB iNB iPM iPB iPBNM iNB iNB iNB iNM iPS iAZ iPBNS iNB iNB iNM iNS iAZ iPS iPMAZ iPB iPM iPS iAZ iNS iNM iNBPS iNM iNS iAZ iPS iPM iPB iPBPM iNB iAZ iNS iPM iPB iPB iPBPB iNB iNB iNM iPB iPB iPB iPB

In Figure 3, it can be observed that PD fuzzy generates the its output variable in the stage ofdefuzzification. At this stage, a linear and time-invariant model is determined using Takagi-Sugeno fuzzy method [18].

The its variable is obtained by a weighted average in Eq. (1), in which the terms itsx, itsy and itsz are

expressed by Eq. (2), Eq. (3) and Eq. (4), respectively. This equation consists of linear functionsdefined from the consequents of the control rules and of the numerical values of the inputvariables Error and Derror.

iPS iPM iPBiAZ iNS iNM iNB

iiii

tsztsytsx

ts++++++

++

= (1)

)5.01.0()3.02.0()1.05.0( Derror Error iNS Derror Error iNM Derror Error iNBitsx ×−×+×−×+×−×= (2)

)0.12.0( Derror Error iAZ itsy ×−×= (3)

)5.01.0()3.02.0()1.05.0( Derror Error iPS Derror Error iPM Derror Error iPBitsz ×−×+×−×+×−×= (4)

From the complex model of representation of a three-phase induction machine, the currentcontroller was developed applying the control quadrature with referential in rotor flux (b).

'

( )b br s s

l I V

s

σ

η =

+

(5)

2

1

s r ml l l

σ =−

(6)

2m

r s

r

ll R

σ η σ

τ = +

(7)


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1

4i pv r

k T l σ

= (8)

ii pik k η = (9)

2.2. Estimation System

The complex model of representation of the three-phase induction machine was applied for thedevelopment of the estimation project of the electromagnetic torque of the three-phase inductionmotor, using control quadrature with fixed reference in the stator (a) and applying an ANN of theLMS algorithm type.

Initially, for the estimation of the electromagnetic torque, it was estimated the stator flux of thethree-phase induction motor.

( )∫ −= dt i Rva

s

a

sd

a

sd sdλ (10)

( )∫ −= dt i Rva

s

a

sq

a

sq sqλ (11)

Due to the occurrence of continuous current levels, called offset, in measuring voltages andcurrents of the motor, caused by the analog components and by the amplifier circuits constitutingthe voltage and current sensors, offset arose in sign of the counter-electromotive force.

To the elimination of offset in this signal, it was developed a neural adaptive filter, by the

technique of LMS algorithm. A neural structure was implemented for each component of thecounter-electromotive force, d and q, similarly.


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Figure 6. LMS adaptive filtering of the counter-electromotive force

Figure 7. LMS adaptive filtering of the estimated stator flux

)(2 n yasd asdf −= λ λ (12)a

sdf n yn y µλ 2)()1( 22 +=+ (13)

In Eq. (13), the learning rates µ of 0.0001, 0.0005 and 0.001 were used due to the specific feedrates applied for the machinings of steel, brass and nylon, respectively.

After the estimation of the stator flux and the elimination of offsets, it was estimated theelectromagnetic torque of the motor of the milling machine using Eq. (14). In this equation, theestimated electromagnetic torque ceest was determined using the estimated stator flux filtered, thestator current and the constant of the number of pole pairs P of the motor, which is equal to two.

( )asqf

a

sd

a

sdf

a

sqest iiPce λ λ −= (14)

3. EXPERIMENTAL RESULTS

To perform the machining of specimens of steel/brass and steel/nylon, the X base was driven withreference signals of position step type of positive and negative amplitudes, resulting indisplacements of this base in right and left directions, respectively, with referential in front ofmilling machine.


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From the signal of estimation of the electromagnetic torque of the motor of the X base in themachining of materials of the specimens, this base was driven with references of specific feedrates.

These references of speed were set for the operational conditions of machining of materials in themilling machine, with a rotation of the cutting tool of 1500 rpm, at a cutting depth of 2 mm inrelation to the specimen surface, and work penetration of 6.35 mm, which corresponds to thediameter of the milling cutter. Therefore, for machinings of steel, brass and nylon, the feed ratereferences set were, in module, 1.6 mm/s, 5.6 mm/s and 8.0 mm/s, respectively.

In Table 2, the average values of estimated electromagnetic torques ceest and the respective feedrate references v* of the X base are presented.

In this table, in steel machining, the average values of torque ceest of 0.42 Nm and of -0.17 Nmwere verified when driving the X base to the right and to the left, respectively.

Table 2. Estimated electromagnetic torques and reference speeds.

Displacement direction Material ce

est (Nm)v*

(mm/s)right steel 0.42 1.6right brass 0.90 5.6left steel -0.17 -1.6left nylon -0.22 -8.0

At the initial instant operating of the system, the specimens were positioned 4 mm to 6 mm awayfrom the milling cutter. The system was driven on empty since the departure of the system untilthe specimen reaches the milling cutter.

3.1. First Experiment

Initially, the curves of response and of reference of the position variable of the X base are

presented in Figure 8. In this test, the X base was driven with a reference signal of step type withamplitude of 77 mm, performing the machining of the steel/brass specimen. By analyzing theresponse curve obtained, there was a settling time of 32.36 s, a steady-state error of 0.12 % andnon-occurrence of overshoot.

0 5 10 15 20 25 30 35 40 450

10

20

30

40

50

60

70

80

Time (s)

S ,

S *

( m m )

S

S*

Figure 8. Response and reference curves of the position of X base


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Then, in Figure 9, the reference curve of feed rate of the X base and the response curve obtainedare presented. As the system functioned initially empty, to drive the X base was applied a signalof the type speed ramp with amplitude of 1.28 mm/s, keeping constant speed until the instant of8.64 s.

From this instant, due to the estimation of the electromagnetic torque obtained in steel machining,a speed ramp with amplitude of 1.6 mm/s was observed at an interval of 0.1 s and remainedconstant until 25.29 s. At that instant, a speed ramp with amplitude of 5.6 mm/s was verified at aninterval of 0.1 s, due to the estimated electromagnetic torque obtained in the brass machining, andthe speed remained constant until a driving v* by null value, resulting thereby in the braking ofthe X base. Based on the analysis of Figure 9, there were null steady-state errors, in the timeintervals in which speed references were constants, and non-occurrence of overshoots.

0 5 10 15 20 25 30 35 40 45-1

0

1

2

3

4

5

6

Time (s)

v , v

* ( m

m / s )

v

v*

Figure 9. Response and reference curves of the feed rate of X base

For analysis of neural estimation of the electromagnetic torque of the three-phase induction motorof the X base, in Figure 10, a curve of the estimated electromagnetic torque ceest obtained in the

machining of the steel/brass specimen was observed. In this graph, it was verified an averagevalue of torque ceest of 0.42 Nm in steel machining, in the range of 8.64 s to 25.29 s, and anaverage value of ceest of 0.90 Nm in the brass machining, in the range of 25.29 s to 32.49 s.

5 10 15 20 25 30 35 40 45-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (s)

c e e s t

( N m )

ceest

Figure 10. Curve of the estimated electromagnetic torque


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3.2. Second Experiment

For machining the steel/nylon specimen, the X base was driven with a reference signal of steptype with amplitude of -46 mm, as shown in the response and reference curves of the position ofX base in Figure 11. In this graph, there was a settling time of 24.76 s, a steady-state error of 0.20

% and non-occurrence of overshoot.

0 5 10 15 20 25 30 35-50

-40

-30

-20

-10

0

Time (s)

S ,

S *

( m m )

S

S*

Figure 11. Response and reference curves of the position of X base

In Figure 12, the reference curve of the feed rate of X base and the response curve obtained arepresented. Initially, it was observed a signal of the type speed ramp with amplitude of -1.28mm/s, keeping this speed constant. At the instant of 8.68 s, due to the torque ceest obtained in thesteel machining, there was a speed ramp with amplitude of -1.6 mm/s, which remained constantuntil 23.17 s. From this instant, it was verified a speed ramp with amplitude of -8.0 mm/s, due tothe torque ceest obtained in the nylon machining, and this amplitude remained constant untilreaching the desired position. By the analysis of Figure 12, there were null steady-state errors, inthe time intervals in which speed references were constants, and non-occurrence of overshoots.

0 5 10 15 20 25 30 35-10

-8

-6

-4

-2

0

2

Time (s)

v , v

* (

m m / s )

v

v*

Figure 12. Response and reference curves of the feed rate of X base

In Figure 13, the curve of the estimated electromagnetic torque of the motor of X base ispresented in the machining of the steel/nylon specimen. In this graph, it was observed an averagevalue of ceest of -0.17 Nm in steel machining, in the range of 8.68 s to 23.17 s, and an averagevalue of ceest of -0.22 Nm in the nylon machining, in the range of 23.17 s to 24.78 s.


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5 10 15 20 25 30 35-0.25

-0.2

-0.15

-0.1

-0.05

0

Time (s)

c e e s t (

N m )

ceest

Figure 13. Curve of the estimated electromagnetic torque

4. CONCLUSIONS

In this work, the controls of position and of feed rate of a milling machine were presentedapplying, automatically, specific feed rates when machining the materials.

Through the response curves of the two experiments, for position, it was verified a maximumsteady-state error of 0.20 %, with no overshoots in any of the machining processes. By observingthe feed rate curves, the fuzzy controller provided the obtaining of null steady-state errors in bothexperiments, in the intervals driving with constant speeds, not occurring overshoots.

The modeling of the speed controller by Takagi-Sugeno fuzzy technique made possible the feedrate control not only in the machining of hard materials, such as steel and brass, but also in themachining of soft material, such as nylon, controlling this speed in permanent and transientregimes, when changing from one type of material to another.

The applications of the neural technique of LMS algorithm in the estimations of the stator fluxespossibilited estimate the electromagnetic torques of the motor of the milling machine simply andeffectively. In the estimations of torque, the convergence of the two ceest signals was observed.

Through the performances of machining processes carried out, it was verified the functionalityand effectiveness of the developed control strategy. Once, from the estimation of theelectromagnetic torque of the milling machine motor in the machining of the specimen materials,it was possible to machine each material with specific feed rate for its cut.

As the results obtained were coherent, presenting the expected performances, it is concluded thatthe control strategy developed for milling machine of this work was very effective in themachining of different types of materials in the same process.

A perspective for future work is to develop a strategy for the controls of cutting speed and of feedrate of a machining system, allowing machining, continuously, a piece constituted by differenttypes of materials.


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REFERENCES

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piecewise variable feedrate scheduling based on the force system model”, International Journal of

Machine Tools & Manufacture, vol. 44, pp. 21–28, 2004.[3] H. Saglam, S. Yaldiz, and F. Unsacar, “The effect of tool geometry and cutting speed on main cuttingforce and tool tip temperature”, Materials and Design, Konya, Turkey, vol. 28, pp. 101-111, 2007.

[4] L. Mao-Yue, F. Hong-Ya, L. Yuan, et al., “An intelligent controller based on constant cutting forcefor 5-axis milling”, IEEE Computer Society, International Conference on Information Technologyand Computer Science, pp. 237-241, 2009.

[5] Y. Wang, L. Xiao, S. Zeng, et al., “An optimal feedrate model and solution for high-speed machiningof small line blocks with look-ahead”, University of Shanghai Jiaotong, Shanghai, China, 2004.

[6] Q. Li, and X. Yin, “Study on adaptive control method of feedrate based on CAM”, IEEE Institute ofElectrical and Electronics Engineers, 2010.

[7] J. A. T. Altuna, “Implementation of the direct method of vector control of an induction motor withstator flux orientation using DSP”, M.S. thesis, State University of Campinas, Campinas, SP, Brazil,1997.

[8] C. O. Affonso, “Neural networks applied in wood machining processes”, Ph.D. dissertation, Facultyof Engineering of Campus Guaratinguetá, Paulista State University, Guaratinguetá, SP, Brazil, 2013.

[9] L. A. Mozelli, “Fuzzy control for Takagi-Sugeno systems: improved conditions and applications”,M.S. thesis, Federal University of Minas Gerais, Belo Horizonte, MG, Brazil, 2008.

[10] I. S. Shaw, and M. G. Simões, Control and Modelling Fuzzy, São Paulo, SP, Brazil: Publisher EdgardBlucher Ltda, 2004.

[11] H. Huang, A. Li, and L. Xu, “Fuzzy control of milling process with constraint of spindle power”,IEEE - Proceedings of the 7th World Congress on Intelligent Control and Automation, pp. 7936 –7939, 2008.

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thesis, National Institute for Space Research, São José dos Campos, SP, Brazil, 2009.[17] H. V. D. Linden Filho, “Application of an adaptive neural filter network in order to cut off the DC

component to estimate the electromagnetic torque of three-phase induction motors”, M.S. thesis,Federal University of Paraíba, João Pessoa, PB, Brazil, 2012.

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FUZZY CONTROLLER AND NEURAL ESTIMATOR APPLIED TO CONTROL A SYSTEM POWERED BY THREE-PHASE INDUCTION MOTOR